Planimeter for computing forces



Feb. 9, 1932. 1 w. SCHWEYDAR 1,344,905

I PLANIMETER FOR COMPUTING FORCES Filed April 6, 1929 3 Sheets-Sheet l aomey Feb. 9, 1932.

w. SCHWEYDAR 1,844,905

PLANIMETER FOR COMPUTING FORCES I 7 Filed April 6, 1929 3 Sheets-Sheet 2Patented Feb. 9, 1932 UNITED STATES PATENT OFFICE W'ILHELM SCHWEYDAB, OFPOTSDAM, GERMANY, ASSIGNOR TO ASKANIA-WERKE A.-G.

VORM CENTRALWERKSTATT DESSAU UN D CARL BAQMBERG FR IEDEN AU, OF BERLIN-FRIEDENAU, GERMANY PLANIMETER FOR COMPUTING FORCES Application filedApril 6, 1929, Serial No. 353,108, and in Germany December 29, 1927.

The present invention relates to a device which makes it possible tosolve, mechanically, integrals of the form fr sin wdm, wherein thequantity 7' denotes the distance of any point P from the origin of arectangular system of coordinates and m the angle between the line OPand one of the axes of the said system of coordinates. Such integralsoccur, for instance, in calculating the gravitation of bodies of anyshape, but the device forming the object of the invention may, ofcourse,be used for any other purpose desired, wherein integrals of the typementioned must be evaluated.

The drawings show byway of example a number ofembodiments of theinvention, wherein Figures 1 and 2 are diagrammatic sketches serving toexplain the different construction of the device,

Fig. 2a is a side view, partly in section,

principles of showing a detail of Fig. 2,

Fig. 2b is a by Fig. 2a,

Fig. 3 is a plan view of a practical embodiment ofthe inventionconstructed in ac cordance with the principles shown in Fig. 1,

Fig. 4 is a side elevation, partly broken away, of Fig. 3,

Fig. .5 shows another practical embodi- Inent constructed in accordancewith the principle of Fig. 2 in side elevation and partly in section,and

Fig. 6 is a plan view of the device shown by Fig. 5.

In Fig. 1, is denotes the sectional area of any body of any position andany extent. That sectional area must be supposed, to be plan View ofthedevice shown very small in proportion to the length of that body. Thepoint 0 may be assumed as representing the origin of a coordinatesystem, the X- and Z-axes of which lie in the plane of the sheet ofdrawing, whereas the Y-axis extends parallel to the greatestlongitudinal extent of the respective body.

On a rotary axle passing through the point 0 in the direction of thevertical Y-axis is fastened at its centre a circular 9 disk 33, andconnected with said axle is also nae end of an arm 34 on which a slideguided parallel to the X axis.

bearing a tracing pin P can be shifted. A bar 35 is so coupled with saidpin that when this latter is moved along the boundary line of anydesired figure said bar is always The bar 35 carries a roll 36, viz theintegrating roll, which contacts with the disk 33 either below or abovethe Z-axis, and the axis of rotation of which lies parallel to theZ-axis. 1f the tracing pin P is shifted along the figure from theposition P to the position P the disk which, as stated, is afiixed tothe same axle to which also the arm 3 is secured is turned through theangle do). Owing to this turning the roll 36 is developed by as much ascorresponds to the amount 9" sin (ode). If the radius of the roll 36 isequal to b and to the. angular part rotation 11, then its entiredevelopment when being moved around the figure K is Inthisconstructional form the circular" disk 33 which is attached to avertical axle extending through the 0-point in the same manner as hasbeen described with respect to the disk 33 of Fig. l is independent ofthe scale of the Figure K and is only small in comparison therewith.There is also in this case a tracing arm 42 secured to said verticalaxle, and extending to both sides from said axle. A slide 3U can beshifted on said arm, and a tracing pin P isaifixed'to this slide, allthis practically as in Fig. 1. On that part of the arm 42 which extendsbeyond the point 0 is provided another slide P which is connected withthe slide P in such a manner-that when the slide 30 is shifted along thearm 42* the distance of the slide 0 from the oint 0 changes in a smallerproportion than that relating to the distance between the tracing pin Pand the oint O. For this purpose the construction illustrated in Figs.2a and 25 may be used. As seen from these figures, a vertical axle 59 issupported on the arm 42a, which carries the slide 30a with the tracingpin P and the slide 30b carrying the member P. The point of the arm4211,

Fig. 2. On the axle 59, two rolls '54 and 55 are rotatably mounted, therolls being rigidly connected with each other. The roll 54 is connectedwith the axle 59 by means of a spiral spring 54a. This spring is woundin'such a manner that it has the tendency to wind the cord 64, which isconnected with an extension 300 of the slide 30a around thecircumference of the roll 54. Around the roll 55, a second cord 65 iswound, the other end of which is connected with an extension P of theslide 30?). This slide 305 is, on the other hand, connected with theadjacent end of the arm 42a by means of a helical spring 56. Therefore,this spring has the tendency to draw the slide 30?) away from the axle59 and to unwind the cord 65 from the roll 55. If the slide 30a,carrying the tracing pin P, is shifted on the arm 42a in such a mannerthat the distance between the pin P and the axle 59 increases, then theroll 54 is rotated by the cord 64 against the action of the spring 54a.The roll 55 is, therefore, also rotated through the same angle and theslide 305 is shifted on the arm 42a under the action of the spring 56 insuch a manner that its distance from the axle 59 increases.

Inversely, if the slide 80a is shifted on the arm 42a, so as to approachthe axle 59, then the spring 5441, which is stronger than the spring 56,releases and effects a rotation of the rolls 54 and 55, whereby the cord64 is wound around the circumference of the roll 54, while the cord 65is wound around the circumference of the roll 55 against the action ofthe spring 56. This slide 306 is, therefore, shifted, so as to approachthe axle 5.9. The lengths of the paths, which the two slides 30a and307) are traversing, correspond to the parts of the circumferences ofthe rolls 54 and 55, from which the cords 64 and 65 have been unwound,or on which the cords have been wound. The lengths of the cords 64 and65 are such that the points defined by the pins P and P would reach thecenter of the axle 59 at the same time and,

therefore, the proportion between the distances of the points P and Pfrom the center of the axle 59 is always the same as the proportionbetween the radii'of the two rolls 54 and 55. 1f, therefore, thedistance between the pin P and the point 0 is 'r', the slide P willalways be kept at a disat which the axle 59 is supported, corresponds tothe point 0 in" tance from-the point 0 which is 0.7, in which equation 0denotes a factor of proportionality which must be so chosen that thepoint P cannot leave the disk. The slide P is connected with a ledge 44to which is at tached a roll 45. These members are equivalents to themembers 35 and 36 in Fig. 1 and arearranged in the same manner as inthis figure. When this device is employed, upon moving the tracing pin Pround the figure K the desired integral is obtained in the proportion c,viz,0fr sin (udw.

\Vith the constructional form shown in Fig. 2 the slide P, or the led e44 and the roll 45 may be arranged, it esired, on the other side of O,that is to say, on the same side as the slide 30, without any change inthe manner of operation of the device.

In Figs. 3 and 4 the detailsof an apparatus designed and operatingaccording to the principle disclosed in Fig. 1 are shown. Figure 3 is aplan of this apparatus and Fig-- ure 4 a transverse sectiontherethrough. 40 denotes a table provided with a bore located inthe'point 0. Through this bore extends an axle 40 which is firmlyconnected with a circular disk 41 located below said table. To the upperend of said axle is afiixed the tracing arm 42 which bears a radiallyshiftable sleeve 4 that is provided with the tracing pin P. The arm 42and the disk 41 are rigidly connected with one another by means of theaxle 4O so that they always turn through the same angle. Parallel to theX- ,axis a double-ledge 44 is arranged and guided alongthe righthand andthe lefthand edge or rim of the table. The double-ledge consists of twoparallel ledges which are rigidly connected with one another but are soarranged with respect to the table 40 that one of them is located abovethe table, the other below the same. The upper-of these ledges isprovided with a longitudinal guide slot and is coupled with the arm 42by means of the pin P which extends through said slot. The lower ledgebears the integration roll 45 which contacts with the circular disk 41.The axle 45 of said roll is supported in bearings 46 in the point 0, aswell as at the rim of the table, parallel with the Z-axis of thecoordinate system.

lVhen moving the tracing pin'roundthe figure K? which represents thesectional area of the body in the earth the integration roll 45 isshifted by means of the guide slot of the ledge 44 in the direction ofthe Z-axis so that its distance from the axis of rotation in the point 0is always 7'- sin a), in which formula r is OP. On the axle 45 of saidroll 45 a counting disk 47 is afiixed near the rim of the table, thisdisk permitting to read. with the aid of a vernier N, the rotation ofthe integration roll 45 which states the value of the integral frsin wdw 6 the principle is that disclosed in Fig. '2.

In these figures 38 denotes a table, and 57 and 57 are two spacedparallel plates arranged above said table and securedto it by a suitablyshaped bracket 39. The two plates are firmly connected with one anotherby bolts 58. The plate 57 bears a bearing 48 in which is supportedanaxle 59 to which is aflixed the circular disk 33 which contacts with aroll 45*, viz. with the integration roll. This roll can be shifted on ashaft 60 with which it is coupled by means of feather and groove, Theshaft 60 is supported in bearings 61 and 61 and extends in the directionof the Z-axis. At one end of this shaft a counting disk 62 is providedwhich indicates the rotation of the integration roll; the rotation canbe read oil with the aid of a Vernier 63 afiixed to the bearing 61. Theroll 45* is attached to a ledge 50 which is connected in turn withanother ledge 50 arranged parallel to the ledge 50. These two ledges liealways parallel to the X-axis and are guided by sleeves 51 which areshiftable on rods 52 of circular transverse section. To the axle 59 ofthe circular disk is aflixed the tracing arm 42 which bears a slide 30with the tracing pin P, as well as a slide 3O having a bolt P. This boltis guided in the slot 50 of the lower ledge 50 From the slide 30 a cordpasses to a drum 54 supported loosely upon the axle 59 and subjectedcentrally to the action of a spring so that when the slide 30 is shiftedin the direction toward the point 0 of the axle 59 the cord is woundupon said drum. Above that drum another drum 55 having a smaller radiusis located, and is firmly connected with the first-mentioned drum. Fromthe drum 55 a cord 65 extends to the slide 5O which is subjected to theaction of a spring 56, the other end of which is afiixed to the tracingarm 42".v

When the tracing pin P is moved with the slide 30 in the directiontoward the point 0 of the axle 59, the cord Si is wound upon the drum54, and the cord 65 coming from the slide 30 is wound upon the drum 55whereby this slide is drawn toward the point 0 and the integration roll45 is shifted in the direction of the Z-axis. The turning movement ofthe tracing arm 42 and, thus. also of the circular disk 33v causes theroll 45 to turn by a value CI'SID to l a,-

in which 7 denotes the line OP, and w denotes the angle between the arma2" and the X-axis.

The diameter of the drums 54 and 55 is so chosen, as are also the twoportions of the tracing arm 53, that the shifting of the bolt 3'? withthe slide 30 takes place in proportion to the distance of the tracingpin P.

I claim 1. A. calculating device for evaluating the integral fr sin ode,especially for computing the force of gravity for a predeterminingpoint, comprising, in combination, a tracing arm carrying a tracing pinand a circular disk rotatable together around a fixed point; anintegration roll contacting with said disk; an axlebearing said roll;and means slidably arranged on said arm for guiding said roll on itsaxle in such a manner that its distance from the said fixed point alwayscorresponds to the vertical distance between said tracing pin and a linecrossing the said fixed point in a direction perpendicular to the axleof said integration roll.

2. A calculating device for evaluating the integral f 1' sin ode,especially for computing the force of gravlty for a predeterminingpoint, comprising, in combination, a tracing arm carrying a tracing pinand a circular disk rotatable together around a fixed point; apoint-forming member shiftably arranged on said tracing arm; anintegration roll contacting with said disk; an axle bearing saiddistance from the fixed point corresponds to the vertical distancebetween said above named point-forming member which is shittable on saidtracing arm and a line crossing said fixed point in a directionperpendicular to the axle of the integration roll; and a couplingbetween said point-forming member and said tracing pin, the couplingbeing so designed that the distance between the said member and saidfixed point is always propor tional to the distance between the saidtracing pin and the said fixed point.

3. A calculating device for evaluating the integral fr sin ode,especially for computing the force of gravity for a predeterminingpoint, comprising, in combination, a table; a tracing arm and a circulardisk rotatable below said table around a fixed point, said tracing armbeing arranged above the table and-

